Numerical study of Phan-Thien–Tanner viscoelastic fluid flow around a two-dimensional circular cylinder at a low Reynolds number: a new classification for drag variations regimes

This study numerically investigates a low Reynolds two-dimensional flow of a viscoelastic fluid over a circular cylinder using the finite volume method. The Phan-Thien–Tanner model, as one of the most accurate non-linear models, for the first time, describes the viscoelastic behavior of a high concentration polymer solution in the flow over a cylinder in high elastic regime in Re = 10. To avoid divergence and to stabilize the numerical process in high elastic cases, the log-conformation approach proposed by previous researchers is used. The convective terms of the equations are discretized using a high-resolution scheme. The physical instability, as observed by some researchers in the creeping regime of high De flow, is very weak in the cases of this research. The numerical results of this research show both drag reduction (for the elasticity number El < 0.025) and drag enhancement (for elasticity number El > 0.025). Compared with the dissipative nature of viscoelastic fluid flows, the drag coefficient, resulted from the polymeric portion of stress, in the high elastic flow regime (El > 10), approached to zero due to an increase in the storing nature of viscoelastic fluid. At these elasticity numbers, the drag coefficient remains constant with El, and the material behaves like a Newtonian fluid. Compared with the shear-thinning behavior and unlike the creeping flow, the elasticity is the main cause of drag variation in most cases. Shear stress affects the drag force directly, while normal stress influences the drag force by changing the pressure distribution over the cylinder. The maximum normal stress occurs at the back of the cylinder due to the wake behind it, while in creeping flow it occurs at its half-front. Finally, the effects of elasticity number, retardation ratio and model parameters on the distribution of stress components, drag coefficient, and vortex dimensions are investigated separately, and a physical discussion is presented.